Towards a Uniied Architecture for Knowledge Representation and Reasoning Based on Terminological Logics

This paper presents a uniied architecture for knowledge representation and reasoning based on terminological (description) logics. The novelty of our approach consists in trying to use description logics not only for representing domain knowledge, but also for describing beliefs, epistemic operators and actions of intelligent agents in an unitary framework. For this purpose , we have chosen a decidable terminological language, called ALC reg + id(C) , whose expres-sivity is high enough to be able to represent actions and epistemic operators corresponding to the majority of modal logics of knowledge and belief. Additionally, we describe practical inference algorithms for the language ALC reg + id(C) which lies at the heart of our RegAL 1 knowledge representation system. The algorithms are sound and complete and can be used directly for deciding the validity and satissability of formulas in the propositional dynamic logic (PDL) by taking advantage of the correspondence between PDL and certain terminological logics 10]. 1 Term subsumption languages Term subsumption languages 2 (TSLs) are descendants of the famous KL-ONE language 4] and can be viewed as formalizations of the frame-based knowledge representation systems. The relationship between TSLs and logic is analogous to the relationship between structured and unstructured programming languages. Indeed, the TSLs impose a certain discipline in the logical structure of a formula (concept) in the very same way in which the structured programming paradigm imposes a discipline in the control structure of a program. Although they somehow restrict 1 The id(C)-Regular closure of the ALC language. 2 Also known as terminological (or description) logics. the expressivity of the description language, TSLs are most of the time preferable to general logic because of their increased understandability and usability in building practical knowledge bases. Also, as opposed to general logic, certain TSLs may possess decidable inference problems while retaining a fairly high expressivity which enables them to represent complex ontologies. The terminological description language usually provides a variety of concept and role constructors, including the boolean operators (conjunction u, disjunction t, maps (R 1 < R 2) and structural descriptions (C : R) are some of the most important concept constructors. We could also mention the following role constructors: id(C) (the restriction of the identity role to the concept C), R ?1 (role inverse), RbC (range restriction), R 1 R 2 (role composition), R (reeexive-transitive closure) and R 1 R 2 (bindings used in structural descriptions). Not all of …